{"id":2580,"date":"2024-02-25T12:58:01","date_gmt":"2024-02-25T12:58:01","guid":{"rendered":"https:\/\/bezwarunku.pl\/?page_id=2580"},"modified":"2024-05-15T10:39:46","modified_gmt":"2024-05-15T09:39:46","slug":"granice-jednostronne-funkcji-i-ciaglosc-funkcji","status":"publish","type":"page","link":"https:\/\/bezwarunku.pl\/index.php\/granice-jednostronne-funkcji-i-ciaglosc-funkcji\/","title":{"rendered":"ci\u0105g\u0142o\u015b\u0107 funkcji"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"2580\" class=\"elementor elementor-2580\" data-elementor-post-type=\"page\">\n\t\t\t\t<header class=\"elementor-element elementor-element-b7edf51 e-con-full e-flex e-con e-parent\" data-id=\"b7edf51\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t<div class=\"elementor-element elementor-element-b074033 e-con-full e-flex e-con e-child\" data-id=\"b074033\" data-element_type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-8508930 elementor-widget elementor-widget-image\" data-id=\"8508930\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/bezwarunku.pl\">\n\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"1170\" height=\"1170\" src=\"https:\/\/bezwarunku.pl\/wp-content\/uploads\/2023\/10\/BEZWARUNKU-1.jpg\" class=\"attachment-full size-full wp-image-39\" alt=\"\" srcset=\"https:\/\/bezwarunku.pl\/wp-content\/uploads\/2023\/10\/BEZWARUNKU-1.jpg 1170w, https:\/\/bezwarunku.pl\/wp-content\/uploads\/2023\/10\/BEZWARUNKU-1-300x300.jpg 300w, https:\/\/bezwarunku.pl\/wp-content\/uploads\/2023\/10\/BEZWARUNKU-1-1024x1024.jpg 1024w, https:\/\/bezwarunku.pl\/wp-content\/uploads\/2023\/10\/BEZWARUNKU-1-150x150.jpg 150w, https:\/\/bezwarunku.pl\/wp-content\/uploads\/2023\/10\/BEZWARUNKU-1-768x768.jpg 768w, https:\/\/bezwarunku.pl\/wp-content\/uploads\/2023\/10\/BEZWARUNKU-1-600x600.jpg 600w, https:\/\/bezwarunku.pl\/wp-content\/uploads\/2023\/10\/BEZWARUNKU-1-100x100.jpg 100w\" sizes=\"(max-width: 1170px) 100vw, 1170px\" \/>\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-0a24747 e-con-full e-flex e-con e-child\" data-id=\"0a24747\" data-element_type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-58e54da elementor-nav-menu--stretch elementor-widget__width-auto elementor-nav-menu__text-align-center elementor-nav-menu--dropdown-tablet elementor-nav-menu--toggle elementor-nav-menu--burger elementor-widget elementor-widget-nav-menu\" data-id=\"58e54da\" data-element_type=\"widget\" data-settings=\"{&quot;full_width&quot;:&quot;stretch&quot;,&quot;layout&quot;:&quot;horizontal&quot;,&quot;submenu_icon&quot;:{&quot;value&quot;:&quot;&lt;svg class=\\&quot;e-font-icon-svg e-fas-caret-down\\&quot; viewBox=\\&quot;0 0 320 512\\&quot; xmlns=\\&quot;http:\\\/\\\/www.w3.org\\\/2000\\\/svg\\&quot;&gt;&lt;path d=\\&quot;M31.3 192h257.3c17.8 0 26.7 21.5 14.1 34.1L174.1 354.8c-7.8 7.8-20.5 7.8-28.3 0L17.2 226.1C4.6 213.5 13.5 192 31.3 192z\\&quot;&gt;&lt;\\\/path&gt;&lt;\\\/svg&gt;&quot;,&quot;library&quot;:&quot;fa-solid&quot;},&quot;toggle&quot;:&quot;burger&quot;}\" data-widget_type=\"nav-menu.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<nav aria-label=\"Menu\" class=\"elementor-nav-menu--main elementor-nav-menu__container elementor-nav-menu--layout-horizontal e--pointer-background e--animation-sweep-right\">\n\t\t\t\t<ul id=\"menu-1-58e54da\" class=\"elementor-nav-menu\"><li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-home menu-item-142\"><a href=\"https:\/\/bezwarunku.pl\/\" class=\"elementor-item\">G\u0141\u00d3WNA<\/a><\/li>\n<li class=\"menu-item menu-item-type-custom menu-item-object-custom menu-item-177\"><a href=\"https:\/\/bezwarunku.pl\/index.php\/wykup-dostep\/\" class=\"elementor-item\">CENNIK<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4681\"><a href=\"https:\/\/bezwarunku.pl\/index.php\/regulamin\/\" class=\"elementor-item\">regulamin<\/a><\/li>\n<\/ul>\t\t\t<\/nav>\n\t\t\t\t\t<div class=\"elementor-menu-toggle\" role=\"button\" tabindex=\"0\" aria-label=\"Menu Toggle\" aria-expanded=\"false\">\n\t\t\t<svg aria-hidden=\"true\" role=\"presentation\" class=\"elementor-menu-toggle__icon--open e-font-icon-svg e-eicon-menu-bar\" viewBox=\"0 0 1000 1000\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M104 333H896C929 333 958 304 958 271S929 208 896 208H104C71 208 42 237 42 271S71 333 104 333ZM104 583H896C929 583 958 554 958 521S929 458 896 458H104C71 458 42 487 42 521S71 583 104 583ZM104 833H896C929 833 958 804 958 771S929 708 896 708H104C71 708 42 737 42 771S71 833 104 833Z\"><\/path><\/svg><svg aria-hidden=\"true\" role=\"presentation\" class=\"elementor-menu-toggle__icon--close e-font-icon-svg e-eicon-close\" viewBox=\"0 0 1000 1000\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M742 167L500 408 258 167C246 154 233 150 217 150 196 150 179 158 167 167 154 179 150 196 150 212 150 229 154 242 171 254L408 500 167 742C138 771 138 800 167 829 196 858 225 858 254 829L496 587 738 829C750 842 767 846 783 846 800 846 817 842 829 829 842 817 846 804 846 783 846 767 842 750 829 737L588 500 833 258C863 229 863 200 833 171 804 137 775 137 742 167Z\"><\/path><\/svg>\t\t\t<span class=\"elementor-screen-only\">Menu<\/span>\n\t\t<\/div>\n\t\t\t\t\t<nav class=\"elementor-nav-menu--dropdown elementor-nav-menu__container\" aria-hidden=\"true\">\n\t\t\t\t<ul id=\"menu-2-58e54da\" class=\"elementor-nav-menu\"><li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-home menu-item-142\"><a href=\"https:\/\/bezwarunku.pl\/\" class=\"elementor-item\" tabindex=\"-1\">G\u0141\u00d3WNA<\/a><\/li>\n<li class=\"menu-item menu-item-type-custom menu-item-object-custom menu-item-177\"><a href=\"https:\/\/bezwarunku.pl\/index.php\/wykup-dostep\/\" class=\"elementor-item\" tabindex=\"-1\">CENNIK<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4681\"><a href=\"https:\/\/bezwarunku.pl\/index.php\/regulamin\/\" class=\"elementor-item\" tabindex=\"-1\">regulamin<\/a><\/li>\n<\/ul>\t\t\t<\/nav>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e735036 elementor-widget__width-auto elementor-widget elementor-widget-button\" data-id=\"e735036\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/bezwarunku.pl\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">zarejestruj si\u0119<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/header>\n\t\t<div class=\"elementor-element elementor-element-9eb95b1 e-con-full e-flex e-con e-parent\" data-id=\"9eb95b1\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-5519b67 elementor-widget elementor-widget-heading\" data-id=\"5519b67\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><a href=\"https:\/\/bezwarunku.pl\/index.php\/analiza-matematyczna\/?preview_id=200&#038;preview_nonce=87c719741f&#038;preview=true\">GRANICE<\/a><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-35a01ff animated-slow elementor-invisible elementor-widget elementor-widget-heading\" data-id=\"35a01ff\" data-element_type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;slideInUp&quot;}\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">ci\u0105g\u0142o\u015b\u0107 funkcji <\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-a878509 e-flex e-con-boxed e-con e-parent\" data-id=\"a878509\" data-element_type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t<div class=\"elementor-element elementor-element-29d3085 e-con-full e-flex e-con e-child\" data-id=\"29d3085\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-8164591 elementor-widget elementor-widget-heading\" data-id=\"8164591\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">FUNKCJE CI\u0104G\u0141E PRZYK\u0141ADY<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-fa24ef7 elementor-widget elementor-widget-image\" data-id=\"fa24ef7\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"548\" height=\"553\" src=\"https:\/\/bezwarunku.pl\/wp-content\/uploads\/2024\/02\/POBIERZ-TERA.png\" class=\"attachment-large size-large wp-image-2586\" alt=\"\" srcset=\"https:\/\/bezwarunku.pl\/wp-content\/uploads\/2024\/02\/POBIERZ-TERA.png 548w, https:\/\/bezwarunku.pl\/wp-content\/uploads\/2024\/02\/POBIERZ-TERA-297x300.png 297w, https:\/\/bezwarunku.pl\/wp-content\/uploads\/2024\/02\/POBIERZ-TERA-150x150.png 150w, https:\/\/bezwarunku.pl\/wp-content\/uploads\/2024\/02\/POBIERZ-TERA-100x100.png 100w\" sizes=\"(max-width: 548px) 100vw, 548px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-b05b5a6 e-con-full e-flex e-con e-child\" data-id=\"b05b5a6\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-6465963 elementor-widget elementor-widget-heading\" data-id=\"6465963\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">FUNKCJE NIECI\u0104G\u0141E PRZYK\u0141ADY<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e1a89d2 elementor-widget elementor-widget-image\" data-id=\"e1a89d2\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"488\" height=\"454\" src=\"https:\/\/bezwarunku.pl\/wp-content\/uploads\/2024\/02\/ZAPISZ-TERA.png\" class=\"attachment-large size-large wp-image-2587\" alt=\"\" srcset=\"https:\/\/bezwarunku.pl\/wp-content\/uploads\/2024\/02\/ZAPISZ-TERA.png 488w, https:\/\/bezwarunku.pl\/wp-content\/uploads\/2024\/02\/ZAPISZ-TERA-300x279.png 300w\" sizes=\"(max-width: 488px) 100vw, 488px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-a2683aa e-flex e-con-boxed e-con e-parent\" data-id=\"a2683aa\" data-element_type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-4e17165 elementor-widget elementor-widget-heading\" data-id=\"4e17165\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h1 class=\"elementor-heading-title elementor-size-default\">$$\\lim_{x\\rightarrow x_0}f\\left(x\\right)=f\\left(x_0\\right)$$<\/h1>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-a7c8009 e-flex e-con-boxed e-con e-parent\" data-id=\"a7c8009\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t<div class=\"elementor-element elementor-element-d69cd9a e-con-full e-flex e-con e-child\" data-id=\"d69cd9a\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-6eb9aa3 elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"6eb9aa3\" data-element_type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"pmpro\"><div class=\"pmpro_card pmpro_content_message\"><div class=\"pmpro_card_content\">nie czekaj d\u0142u\u017cej, wykup pakiet i sprawd\u017a rozwi\u0105zania.<br \/><a href=\"https:\/\/bezwarunku.pl\/index.php\/wykup-dostep\/\">Przed\u0142u\u017c pakiet!<\/a><\/div><div class=\"pmpro_card_actions pmpro_font-medium\">Already a member? <a href=\"https:\/\/bezwarunku.pl\/index.php\/membership-login\/?redirect_to=https%3A%2F%2Fbezwarunku.pl%2Findex.php%2Fgranice-jednostronne-funkcji-i-ciaglosc-funkcji%2F\">Log in here<\/a><\/div><\/div><\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-a22da23 elementor-widget elementor-widget-heading\" data-id=\"a22da23\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">1. Zbadaj ci\u0105g\u0142o\u015b\u0107 funkcji: $$f\\left(x\\right)=\\left\\{\\begin{array}{l}\\frac{x^2-9}{x+3},\\;x\\neq-3\\\\6,\\;x=-3\\end{array}\\right.$$\nw punkcie \\(x_0=-3\\)<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-edd3064 e-con-full e-flex e-con e-child\" data-id=\"edd3064\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-62ef6a5 elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"62ef6a5\" data-element_type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"pmpro\"><div class=\"pmpro_card pmpro_content_message\"><div class=\"pmpro_card_content\">nie czekaj d\u0142u\u017cej, wykup pakiet i sprawd\u017a rozwi\u0105zania.<br \/><a href=\"https:\/\/bezwarunku.pl\/index.php\/wykup-dostep\/\">Przed\u0142u\u017c pakiet!<\/a><\/div><div class=\"pmpro_card_actions pmpro_font-medium\">Already a member? <a href=\"https:\/\/bezwarunku.pl\/index.php\/membership-login\/?redirect_to=https%3A%2F%2Fbezwarunku.pl%2Findex.php%2Fgranice-jednostronne-funkcji-i-ciaglosc-funkcji%2F\">Log in here<\/a><\/div><\/div><\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c445609 elementor-widget elementor-widget-heading\" data-id=\"c445609\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">2. Zbadaj ci\u0105g\u0142o\u015b\u0107 funkcji: $$f\\left(x\\right)=\\left\\{\\begin{array}{l}\\frac{x^3-4x}{x-2},\\;x\\neq2\\\\8,\\;x=2\\end{array}\\right.$$\nw punkcie \\(x_0=2\\)<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-16167d6 e-con-full e-flex e-con e-child\" data-id=\"16167d6\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-ff89625 elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"ff89625\" data-element_type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"pmpro\"><div class=\"pmpro_card pmpro_content_message\"><div class=\"pmpro_card_content\">nie czekaj d\u0142u\u017cej, wykup pakiet i sprawd\u017a rozwi\u0105zania.<br \/><a href=\"https:\/\/bezwarunku.pl\/index.php\/wykup-dostep\/\">Przed\u0142u\u017c pakiet!<\/a><\/div><div class=\"pmpro_card_actions pmpro_font-medium\">Already a member? <a href=\"https:\/\/bezwarunku.pl\/index.php\/membership-login\/?redirect_to=https%3A%2F%2Fbezwarunku.pl%2Findex.php%2Fgranice-jednostronne-funkcji-i-ciaglosc-funkcji%2F\">Log in here<\/a><\/div><\/div><\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5ed8076 elementor-widget elementor-widget-heading\" data-id=\"5ed8076\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">3. Zbadaj ci\u0105g\u0142o\u015b\u0107 funkcji: $$f\\left(x\\right)=\\left\\{\\begin{array}{l}\\frac{x^3-1}{1-x},\\;x\\neq1\\\\-3,\\;x=1\\end{array}\\right.$$\nw punkcie \\(x_0=1\\)<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-427eedc e-con-full e-flex e-con e-child\" data-id=\"427eedc\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-a6e7f77 elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"a6e7f77\" data-element_type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"pmpro\"><div class=\"pmpro_card pmpro_content_message\"><div class=\"pmpro_card_content\">nie czekaj d\u0142u\u017cej, wykup pakiet i sprawd\u017a rozwi\u0105zania.<br \/><a href=\"https:\/\/bezwarunku.pl\/index.php\/wykup-dostep\/\">Przed\u0142u\u017c pakiet!<\/a><\/div><div class=\"pmpro_card_actions pmpro_font-medium\">Already a member? <a href=\"https:\/\/bezwarunku.pl\/index.php\/membership-login\/?redirect_to=https%3A%2F%2Fbezwarunku.pl%2Findex.php%2Fgranice-jednostronne-funkcji-i-ciaglosc-funkcji%2F\">Log in here<\/a><\/div><\/div><\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ebc2e81 elementor-widget elementor-widget-heading\" data-id=\"ebc2e81\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">4. Zbadaj ci\u0105g\u0142o\u015b\u0107 funkcji:$$f\\left(x\\right)=\\left\\{\\begin{array}{l}3+x^2,\\;x\\leq0\\\\\\frac{\\sin\\left(3x\\right)}x,\\;x&gt;0\\end{array}\\right.$$\nw punkcie \\(x_0=0\\)<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-cda1870 e-con-full e-flex e-con e-child\" data-id=\"cda1870\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-f0de35a elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"f0de35a\" data-element_type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"pmpro\"><div class=\"pmpro_card pmpro_content_message\"><div class=\"pmpro_card_content\">nie czekaj d\u0142u\u017cej, wykup pakiet i sprawd\u017a rozwi\u0105zania.<br \/><a href=\"https:\/\/bezwarunku.pl\/index.php\/wykup-dostep\/\">Przed\u0142u\u017c pakiet!<\/a><\/div><div class=\"pmpro_card_actions pmpro_font-medium\">Already a member? <a href=\"https:\/\/bezwarunku.pl\/index.php\/membership-login\/?redirect_to=https%3A%2F%2Fbezwarunku.pl%2Findex.php%2Fgranice-jednostronne-funkcji-i-ciaglosc-funkcji%2F\">Log in here<\/a><\/div><\/div><\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3b8ed60 elementor-widget elementor-widget-heading\" data-id=\"3b8ed60\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">5. Zbadaj ci\u0105g\u0142o\u015b\u0107 funkcji: $$f\\left(x\\right)=\\left\\{\\begin{array}{l}x^2,\\;x\\in(-\\infty,1\\rbrack\\\\2x,\\;x\\in(1,+\\infty)\\end{array}\\right.$$\nw punkcie \\(x_0=1\\)<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-a6b9eed e-con-full e-flex e-con e-child\" data-id=\"a6b9eed\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-b9f8004 elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"b9f8004\" data-element_type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"pmpro\"><div class=\"pmpro_card pmpro_content_message\"><div class=\"pmpro_card_content\">nie czekaj d\u0142u\u017cej, wykup pakiet i sprawd\u017a rozwi\u0105zania.<br \/><a href=\"https:\/\/bezwarunku.pl\/index.php\/wykup-dostep\/\">Przed\u0142u\u017c pakiet!<\/a><\/div><div class=\"pmpro_card_actions pmpro_font-medium\">Already a member? <a href=\"https:\/\/bezwarunku.pl\/index.php\/membership-login\/?redirect_to=https%3A%2F%2Fbezwarunku.pl%2Findex.php%2Fgranice-jednostronne-funkcji-i-ciaglosc-funkcji%2F\">Log in here<\/a><\/div><\/div><\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-75c7f8d elementor-widget elementor-widget-heading\" data-id=\"75c7f8d\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">6. Zbadaj ci\u0105g\u0142o\u015b\u0107 funkcji: $$f\\left(x\\right)=\\left\\{\\begin{array}{l}\\frac{2x-8}{\\sqrt{x-1}-\\sqrt3},\\;x\\neq4\\\\2,\\;x=4\\end{array}\\right.$$\nw punkcie \\(x_0=4\\)<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-39ce29e e-con-full e-flex e-con e-child\" data-id=\"39ce29e\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-9a6d11a elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"9a6d11a\" data-element_type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"pmpro\"><div class=\"pmpro_card pmpro_content_message\"><div class=\"pmpro_card_content\">nie czekaj d\u0142u\u017cej, wykup pakiet i sprawd\u017a rozwi\u0105zania.<br \/><a href=\"https:\/\/bezwarunku.pl\/index.php\/wykup-dostep\/\">Przed\u0142u\u017c pakiet!<\/a><\/div><div class=\"pmpro_card_actions pmpro_font-medium\">Already a member? <a href=\"https:\/\/bezwarunku.pl\/index.php\/membership-login\/?redirect_to=https%3A%2F%2Fbezwarunku.pl%2Findex.php%2Fgranice-jednostronne-funkcji-i-ciaglosc-funkcji%2F\">Log in here<\/a><\/div><\/div><\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-977a766 elementor-widget elementor-widget-heading\" data-id=\"977a766\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">7. Zbadaj ci\u0105g\u0142o\u015b\u0107 funkcji: $$f\\left(x\\right)=\\left\\{\\begin{array}{l}3-x,\\;x\\in(-\\infty,2\\rbrack\\\\\\left(x-1\\right)^2,\\;(2,+\\infty)\\end{array}\\right.$$\nw punkcie \\(x_0=2\\)<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-1c310c2 e-con-full e-flex e-con e-child\" data-id=\"1c310c2\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-d80416a elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"d80416a\" data-element_type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"pmpro\"><div class=\"pmpro_card pmpro_content_message\"><div class=\"pmpro_card_content\">nie czekaj d\u0142u\u017cej, wykup pakiet i sprawd\u017a rozwi\u0105zania.<br \/><a href=\"https:\/\/bezwarunku.pl\/index.php\/wykup-dostep\/\">Przed\u0142u\u017c pakiet!<\/a><\/div><div class=\"pmpro_card_actions pmpro_font-medium\">Already a member? <a href=\"https:\/\/bezwarunku.pl\/index.php\/membership-login\/?redirect_to=https%3A%2F%2Fbezwarunku.pl%2Findex.php%2Fgranice-jednostronne-funkcji-i-ciaglosc-funkcji%2F\">Log in here<\/a><\/div><\/div><\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f4c5546 elementor-widget elementor-widget-heading\" data-id=\"f4c5546\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">8. Zbadaj ci\u0105g\u0142o\u015b\u0107 funkcji: $$f\\left(x\\right)=\\left\\{\\begin{array}{l}x+1,\\;x\\in(-\\infty,0\\rbrack\\\\2-x^2,\\;(0,+\\infty)\\end{array}\\right.$$\nw punkcie \\(x_0=0\\)<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-b831dd2 e-con-full e-flex e-con e-child\" data-id=\"b831dd2\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-265476d elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"265476d\" data-element_type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"pmpro\"><div class=\"pmpro_card pmpro_content_message\"><div class=\"pmpro_card_content\">nie czekaj d\u0142u\u017cej, wykup pakiet i sprawd\u017a rozwi\u0105zania.<br \/><a href=\"https:\/\/bezwarunku.pl\/index.php\/wykup-dostep\/\">Przed\u0142u\u017c pakiet!<\/a><\/div><div class=\"pmpro_card_actions pmpro_font-medium\">Already a member? <a href=\"https:\/\/bezwarunku.pl\/index.php\/membership-login\/?redirect_to=https%3A%2F%2Fbezwarunku.pl%2Findex.php%2Fgranice-jednostronne-funkcji-i-ciaglosc-funkcji%2F\">Log in here<\/a><\/div><\/div><\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5b21498 elementor-widget elementor-widget-heading\" data-id=\"5b21498\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">9. Zbadaj ci\u0105g\u0142o\u015b\u0107 funkcji: $$f\\left(x\\right)=\\left\\{\\begin{array}{l}x^3+1,\\;x\\in(-\\infty,0\\rbrack\\\\\\sqrt x,\\;(0,+\\infty)\\end{array}\\right.$$\nw punkcie \\(x_0=0\\)<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-d44fc3d e-con-full e-flex e-con e-child\" data-id=\"d44fc3d\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-43e8059 elementor-widget__width-initial elementor-widget elementor-widget-toggle\" data-id=\"43e8059\" data-element_type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"pmpro\"><div class=\"pmpro_card pmpro_content_message\"><div class=\"pmpro_card_content\">nie czekaj d\u0142u\u017cej, wykup pakiet i sprawd\u017a rozwi\u0105zania.<br \/><a href=\"https:\/\/bezwarunku.pl\/index.php\/wykup-dostep\/\">Przed\u0142u\u017c pakiet!<\/a><\/div><div class=\"pmpro_card_actions pmpro_font-medium\">Already a member? <a href=\"https:\/\/bezwarunku.pl\/index.php\/membership-login\/?redirect_to=https%3A%2F%2Fbezwarunku.pl%2Findex.php%2Fgranice-jednostronne-funkcji-i-ciaglosc-funkcji%2F\">Log in here<\/a><\/div><\/div><\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6c497bf elementor-widget elementor-widget-heading\" data-id=\"6c497bf\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">10. Zbadaj ci\u0105g\u0142o\u015b\u0107 funkcji: $$f\\left(x\\right)=\\left\\{\\begin{array}{l}\\frac{x^2-2x}{(x-2)^2},\\;x\\neq2\\\\5,\\;x=2\\end{array}\\right.$$\nw punkcie \\(x_0=2\\)<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>zarejestruj si\u0119 GRANICE ci\u0105g\u0142o\u015b\u0107 funkcji FUNKCJE CI\u0104G\u0141E PRZYK\u0141ADY FUNKCJE NIECI\u0104G\u0141E PRZYK\u0141ADY $$lim_{xrightarrow x_0}fleft(xright)=fleft(x_0right)$$ Nie b\u0105d\u017a dziad, wykup pakiet.Przed\u0142\u00f3\u017c pakiet! 1. Zbadaj ci\u0105g\u0142o\u015b\u0107 funkcji: $$fleft(xright)=left{begin{array}{l}frac{x^2-9}{x+3},;xneq-3\\6,;x=-3end{array}right.$$ w punkcie (x_0=-3) Nie b\u0105d\u017a dziad, wykup pakiet.Przed\u0142\u00f3\u017c pakiet! 2. Zbadaj ci\u0105g\u0142o\u015b\u0107 funkcji: $$fleft(xright)=left{begin{array}{l}frac{x^3-4x}{x-2},;xneq2\\8,;x=2end{array}right.$$ w punkcie (x_0=2) Nie b\u0105d\u017a dziad, wykup pakiet.Przed\u0142\u00f3\u017c pakiet! 3. Zbadaj ci\u0105g\u0142o\u015b\u0107 funkcji: $$fleft(xright)=left{begin{array}{l}frac{x^3-1}{1-x},;xneq1\\-3,;x=1end{array}right.$$ w punkcie (x_0=1) [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"templates\/landing.php","meta":{"pmpro_default_level":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_uf_show_specific_survey":0,"_uf_disable_surveys":false,"footnotes":""},"class_list":["post-2580","page","type-page","status-publish","hentry","pmpro-has-access","entry","owp-thumbs-layout-horizontal","owp-btn-normal","owp-tabs-layout-horizontal","has-no-thumbnails","has-product-nav"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/bezwarunku.pl\/index.php\/wp-json\/wp\/v2\/pages\/2580","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/bezwarunku.pl\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/bezwarunku.pl\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/bezwarunku.pl\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/bezwarunku.pl\/index.php\/wp-json\/wp\/v2\/comments?post=2580"}],"version-history":[{"count":116,"href":"https:\/\/bezwarunku.pl\/index.php\/wp-json\/wp\/v2\/pages\/2580\/revisions"}],"predecessor-version":[{"id":4534,"href":"https:\/\/bezwarunku.pl\/index.php\/wp-json\/wp\/v2\/pages\/2580\/revisions\/4534"}],"wp:attachment":[{"href":"https:\/\/bezwarunku.pl\/index.php\/wp-json\/wp\/v2\/media?parent=2580"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}